The DOI matches its Crossref record; 14 of the 14 references it cites were found in a registry or an index; none of the 8 sources its claims cite is checked for support yet.
Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect
Open accessAbstract
We demonstrate that the electronic gap of a graphene bilayer can be controlled externally by applying a gate bias. From the magnetotransport data (Shubnikov-de Haas measurements of the cyclotron mass), and using a tight-binding model, we extract the value of the gap as a function of the electronic density. We show that the gap can be changed from zero to midinfrared energies by using fields of less, approximately < 1 V/nm, below the electric breakdown of SiO2. The opening of a gap is clearly seen in the quantum Hall regime.
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
The paper reports that bilayer graphene can be converted into a semiconductor whose band gap is externally tunable by gate bias, with the gap ranging from zero to mid-infrared energies. Magnetotransport measurements and tight-binding modeling show clear gap signatures, including a zero Hall conductivity plateau and an asymmetric cyclotron mass.
Key findings
- In biased bilayer graphene, a plateau at zero Hall conductivity appears at the neutrality point, unlike the pristine case; the longitudinal resistivity at neutrality exceeded 150 kΩ at 4 K for the biased device, compared with 6 kΩ for the unbiased device under the same conditions.
- The cyclotron mass depends asymmetrically on carrier density, and comparison with tight-binding theory yields an interlayer hopping parameter of 0.22 eV and indicates gaps larger than 0.2 eV.
- A small-bias linear fit to the screened theory gives a gap of about 1.2 meV per volt relative to a gate voltage of 25 V, while the theory predicts gap saturation at the interlayer hopping scale.
- The model agrees well with angle-resolved photoemission data, except in the gap saturation regime around densities of about 50 × 10¹² cm⁻².
Methods
- Bilayer graphene devices were prepared by micromechanical cleavage on 300 nm SiO₂ and patterned into Hall bars; carrier density was controlled by a Si backgate and by NH₃ chemical doping, with transport measured by lock-in techniques in fields up to 12 T and temperatures from 4 to 300 K.
- Shubnikov–de Haas oscillations were measured versus temperature and fitted to extract the cyclotron mass as a function of carrier density.
- The data were interpreted with a Bernal-stacked bilayer tight-binding model using in-plane hopping of 3.1 eV and interlayer hopping of 0.22 eV, including a self-consistent Hartree treatment of screening; Hall conductivity was modeled for a zigzag-edged ribbon in a magnetic field.
Limitations
- The paper states that the Hartree approach is reliable only when the gap is small compared with the interlayer hopping; for hole doping it underestimates the cyclotron mass while the unscreened model overestimates it, so the true gap lies between these limits and a better screening treatment is needed when the electrostatic energy becomes comparable to the interlayer hopping.
- The paper notes that the comparison with angle-resolved photoemission data works well except in the gap saturation regime at high density.
- Evident from the text: for the transport devices, the gap values are inferred by fitting a tight-binding/Hartree model to magnetotransport rather than measured directly by a spectroscopic probe.
Model-written summary. Check it against the paper before relying on it.
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Claims the paper makes
19 Own result · 18 Own interpretation · 8 Sources not found · 4 No basis given
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The opening of a gap is clearly seen in the quantum Hall regime.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
boosted- Asserted: passes — The authors put it forward as true.
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In the paper
“which is absent in the unbiased case”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“by comparing the observed behavior with our tightbinding results, we show that the gap can be tuned to values larger than 0.2 eV”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“in the biased device, xx at n 0 exceeded 150 kOhm at 4 K, as compared to 6 kOhm for the unbiased case under the same conditions”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“in a magnetic field, a pronounced plateau at zero Hall conductivity xy 0 is found for the biased bilayer”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“the cyclotron mass, m c , in the bilayer biased by chemical doping is an asymmetric function of carrier density, n”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“The linear increase of m c with jnj and the pronounced asymmetry between hole-and electron-doping of the biased bilayer are clearly seen here.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
boosteddirect- Asserted: passes — The authors put it forward as true.
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In the paper
“We show that the gap can be changed from zero to midinfrared energies by using fields of & 1 V=nm, below the electric breakdown of SiO 2 .”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Rests on an assumption: The breakdown field for SiO2 is 1 V/nm (i.e., 300 V for the used oxide thickness).
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The linear increase of m c with jnj and the pronounced asymmetry between hole-and electron-doping of the biased bilayer are clearly seen here.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
boostedcorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“The energy gap is revealed by the appearance of the N 0 plateau at xy 0 [see the curve labeled ''doped'' in Fig. 1(a)].”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
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- It may state two separate claims as one. 10
- The quote only partly states this claim. 2
- Probably not a substantial claim. 1
In the paper
“The N 0 plateau is strikingly absent, so that a double step of 8e 2 =h in height occurs at n 0, indicating a metallic state at the neutrality point [3].”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
What the sources say
- Not matchedcites [3] 3. K. S. Novoselov et al., Nature Phys. 2, 177 (2006).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
hedgeddirect- Asserted: passes — The authors put it forward as true.
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- Not matched
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In the paper
“In this case two flat bands with energies ÿeV=2 and eV=2 appear, similar to the case of zero magnetic field.The other two zero energy bands become dispersive inside the gap, showing the band-crossing phenomenon.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“In the hole doping region in Fig. 1(b), the Hartree approach underestimates the value of m c whereas the simple unscreened result overestimates it.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
plaincorrelational- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The emerged plateau was accompanied by a huge peak in longitudinal resistivity xx , indicating an insulating state”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“which provides a clear signature of a gap and allows its estimate”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
boostedcorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“we have cross-checked our theory against angle-resolved photoemission spectroscopy (ARPES) data [8] and found excellent agreement.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
What the sources say
- Not matchedcites [8] 8. Theory of the gap opening within the continuum model was previously given by E. McCann, Phys. Rev. B 74, 161403 (2006).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaincorrelational- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Zero potential difference and zero gap are expected at n 2n 0 in both unscreened and screened cases, as seen from Eqs. (1) and ( 2) and the fact that nn; 0 0.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- The authors state this as an assumption: The charge in layers 1 and 2 of the bilayer is equal to -ne/2.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Note that at the zero Hall plateau the current carried around the ribbon loop is zero, I 0, which implies, from the theory view point, a diverging longitudinal resistivity at low T”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“This opens a gap of eV in size.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“At this particular density the gap closes and the theoretical value becomes independent of the screening assumptions.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one. The quote only partly states this claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“a more accurate treatment of screening is needed when eV becomes of the order of t ? .”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“The coefficient 7:2 10 10 cm ÿ2 =V is determined by the geometry of the resulting capacitor and is in agreement with the values of n 1 found experimentally [1][2][3].”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
What the sources say
- Not matchedcites [1][2][3]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
The authors state this as an assumption.
The charge in layers 1 and 2 of the bilayer is equal to -ne/2.
“Assuming equal charge ÿne=2 in layers 1 and 2 of the bilayer”
The paper relies on this without support.
The breakdown field for SiO2 is 1 V/nm (i.e., 300 V for the used oxide thickness).
“Note that the breakdown field for SiO 2 is 1 V=nm (i.e., 300 V for the used oxide thickness)”
The authors state this as an assumption.
The electric field induced between the two layers can be considered as a result of the effect of charged surfaces placed above and below bilayer graphene.
“The electric field induced between the two layers can be considered as a result of the effect of charged surfaces placed above and below bilayer graphene .”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > Abstract
“As pointed out by Laughlin [14], changing the magnetic flux through the ribbon loop by a flux quantum causes the states to move rigidly towards one edge.”
§ Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect > References
“14. The unbiased case, in the continuum approximation, was studied in Ref. [5]. 15. R. B. Laughlin, Phys. Rev. B 23, 5632 (1981).”
Citations
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Self-citationExperimental observation of the quantum Hall effect and Berry's phase in graphene
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Schedin, F., Geim, A. K., Morozov, S. V., Hill, E. W., Blake, P., Katsnelson, M. I., & Novoselov, K. S. (2007) · Nature Materials · doi:10.1038/nmat1967 · Cited by 8,028
Self-citationControlling the Electronic Structure of Bilayer Graphene
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Pseudospin–orbital coupling for pseudospintronic device in graphene
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A TDDFT Investigation on Plasmons in Multilayer Graphene Nanostructures
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“These latent advantages brought a great interest in investigation of AB graphene [2, 5].”
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A Simulation-Based Investigation of Cu_2ZnSnS_4 Solar Cells with Graphene as a Window Layer
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Symmetry effect on the mechanism of the optical absorption of phosphorene quantum dots
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X-ray edge singularity of bilayer graphene
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Electron tunneling in a vertical graphene heterostructure
Yan, Y., & Zhao, H. (2013) · The European Physical Journal B · doi:10.1140/epjb/e2013-30833-9 · Cited by 3
Spin-dependent group delay time and Hartman effect in ferromagnetic bilayer graphene superlattice
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Probing valley phenomena with gate-defined valley splitters
Luna, J. D. T., Vilkelis, K., & Manesco, A. L. R. (2025) · SciPost Physics · doi:10.21468/scipostphys.18.2.062 · Cited by 8
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Li, Y.-Q., Zhang, H., & Liu, D. (2016) · Modern Physics Letters B · doi:10.1142/s0217984916501815 · Cited by 3
Wang, X., Cui, Y., Huo, X., et al. (2023) · Journal of Materials Science · doi:10.1007/s10853-023-08780-1 · Cited by 3
“[16] Castro EV, Novoselov KS, Morozov SV et al (2007) Biased bilayer graphene: semiconductor with a gap tunable by the”
BackgroundTunable Excitons in Bilayer Graphene with Opened Energy Gap
Avetisyan, A. A., Djotyan, A. P., & Moulopoulos, K. (2018) · Physics of Atomic Nuclei · doi:10.1134/s1063778818060042 · Cited by 4
Dynamical freezing and switching in periodically driven bilayer graphene
Sasidharan, S., & Surendran, N. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.174301 · Cited by 3
Spin-polarized current state of electrons in bilayer graphene
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Coulomb-blockade peak spacing statistics of graphene quantum dots on SiO2
Herrmann, O., Gould, C., & Molenkamp, L. W. (2016) · Journal of Applied Physics · doi:10.1063/1.4965303 · Cited by 3
Zhao, P.-L., Yu, J. Z., Zhong, H., et al. (2020) · Radboud Repository (Radboud University) · Cited by 3
On the Singular Effects in the Relativistic Landau Levels in Graphene with a Disclination*
Nascimento, R. F. D., Cogollo, D., Silva, E. O., et al. (2018) · Communications in Theoretical Physics · doi:10.1088/0253-6102/70/6/817 · Cited by 3
Electronic structure and optical properties of Graphene MonoxidePreprint
Yang, G., Zhang, Y., & Yan, X.-W. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1209.0555 · Cited by 3
Phonon-induced renormalization of the electron spectrum of biased bilayer graphene
Kryuchkov, S. V., & Kukhar, E. I. (2018) · Superlattices and Microstructures · doi:10.1016/j.spmi.2018.03.050 · Cited by 3
Sun, J. C., Xu, L., & Zhang, J. (2020) · Modern Physics Letters B · doi:10.1142/s0217984920501808 · Cited by 3
Elshazly, M. K., Huzayyin, A., & Dawson, F. P. (2023) · The Journal of Chemical Physics · doi:10.1063/5.0177808 · Cited by 3
Width effects on bilayer graphene nanoribbon polarons
Logrado, A. L., Cassiano, T. D. S. A., da Cunha, W. F., et al. (2024) · Physical Chemistry Chemical Physics · doi:10.1039/d4cp00760c · Cited by 3
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Optical Properties of Graphene in Magnetic and Electric fieldsPreprint
Lin, C., Do, T.-N., Huang, Y.-K., et al. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1603.02797 · Cited by 3
“Under an electric field, the bilayer graphene shows a sharp peak due to new transition channels within the energy gap (up to 100 meV) [96, 97, 101, 103], and the cases of more than three layers display enhanced semimetal characteristics attributed to the significant overlap of the lowenergy subbands [95,103,104,108].”
BackgroundElectric field response in bilayer graphene: Ab initio investigation
Mori, Y., Minamitani, E., Ando, Y., et al. (2016) · Applied Physics Express · doi:10.7567/apex.9.115104 · Cited by 3
Study the metal-insulator transitions of bilayer graphene: Abelian group schemes approach
Behnia, S., Habibpourbisafar, R., & Rahimi, F. (2020) · Superlattices and Microstructures · doi:10.1016/j.spmi.2020.106498 · Cited by 3
Sliding-induced topological transitions in bilayer biphenylene
Lage, L. L., Bravo, S., Arroyo-Gascón, O., et al. (2025) · 2D Materials · doi:10.1088/2053-1583/ae2522 · Cited by 3
“By introducing a gate voltage between the layers, in the AB case a band gap can be achieved [10].”
Counting molecular-beam grown graphene layers
Plaut, A. S., Wurstbauer, U., Pinczuk, A., et al. (2013) · Applied Physics Letters · doi:10.1063/1.4811708 · Cited by 3
Vali, M., & Bayani, A. H. (2025) · Materials Science in Semiconductor Processing · doi:10.1016/j.mssp.2025.109599 · Cited by 3
Electronic structure of trilayer graphene with internal layer broken
Jaskólski, W. (2021) · Molecular Physics · doi:10.1080/00268976.2021.2013554 · Cited by 3
Electric field driven self-assembly of dissolved graphene foam particles in a capillary
Wiewiórski, P., Stręk, W., Tomala, R. A., et al. (2023) · Materials Letters · doi:10.1016/j.matlet.2023.133851 · Cited by 3
Li, W., & Zhang, S. (2025) · Journal of Electronic Materials · doi:10.1007/s11664-025-12078-0 · Cited by 3
Theory of field-modulated spin valley orbital pseudospin physics
Chen, F.-W., & Wu, Y.-S. G. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.013076 · Cited by 3
Persistent currents in topological and trivial confinement in silicene
Jurkowski, P., & Szafran, B. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.101.075408 · Cited by 3
Recent progresses on artificial graphene quantum dots
Zhou, X., & He, L. (2025) · Fundamental Research · doi:10.1016/j.fmre.2025.03.020 · Cited by 3
Asymmetric bilayer graphene nanoribbon MOSFETs for analog and digital electronics
Dinarvand, A., Ahmadi, V., & Darvish, G. (2016) · Superlattices and Microstructures · doi:10.1016/j.spmi.2016.03.034 · Cited by 3
The Origin of BC 7 Sheet Metallicity and the Tuning of its Electronic Properties by Hydrogenation
Lei, X., Liu, G., Wu, M., Xu, B., Ouyang, C., & Pan, B. (2013) · Chinese Physics Letters · doi:10.1088/0256-307x/30/6/066102 · Cited by 3
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“This is because bilayer graphene is considered equally important as monolayer graphene for both technological applications and fundamental scientific research [4, 9] due to its distinct electronic properties.”
BackgroundThe effect of uniaxial strain on graphene nanoribbon carrier statistic
Johari, Z., & Ismail, R. (2013) · Nanoscale Research Letters · doi:10.1186/1556-276x-8-479 · Cited by 3
Demonstration of magnetic confinement in graphene with Fano-type resonances
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Regulation of transport properties by polytypism: a computational study on bilayer MoS 2
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A new physics-based compact model for Bilayer Graphene Field-Effect Transistors
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Voltage tunable plasmon propagation in dual gated bilayer graphene
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Structural And Electronic Properties of Two-Dimensional Silicene, Graphene, and Related Structures
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Spin-orbit coupling and the Landau level spectrum of ABA-stacked trilayer graphene
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Electrical properties of in-plane-implanted graphite nanoribbons
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Characteristic Variations of Graphene Field-Effect Transistors Induced by CF4 Gas
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Effect of asymmetric Fermi velocity on trigonally warped spectrum of bilayer graphene
Adinehvand, F., & Cheraghchi, H. (2017) · Journal of Physics and Chemistry of Solids · doi:10.1016/j.jpcs.2017.04.003 · Cited by 2
Novel two-dimensional materials and their heterostructures constructed in ultra-high vacuum
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Substrate-induced bandgap in the spectrum of an epitaxial graphene layer
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Strain-Tuneable Bipolaron Stability on Ultranarrow Bilayer Graphene Nanoribbon
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“It has been experimentally verified that the main characteristics of graphene related 2D materials are governed by the geometric structure and external electric and magnetic fields [25–27].”
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Structural modulation of bilayer graphene under an external electric field and carrier doping
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Impact Ionization Rate of Electrons in Bilayer Graphene Nanoribbons
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Promises and Challenges of Unconventional Electrocatalyst Supports
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“Despite its amazing electrical properties, graphene could not successfully implement in an effective field effect transistor because of its zero band gap [3].”
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“While unbiased bilayer graphene is semi-metallic, inversion symmetry can be broken by applying an electric field across the graphene layers, for example, resulting in the opening of a bandgap [22–24], and the ability to support excitons that can be spectrally tuned with the applied bias [15–21].”
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Metadata
- Authors
- Castro, E. V., Novoselov, K. S., Morozov, S. V., Peres, N. M. R., dos Santos, J. M. B. L., Nilsson, J., Guinea, F., Geim, A. K., & Neto, A. H. C.
- Affiliations
- Universidade do Porto (PT)
- University of Manchester (GB)
- University of Minho (PT)
- Boston University (US)
- Consejo Superior de Investigaciones Científicas (ES)
- ORCID
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2007-11-20
- Volume
- 99
- Issue
- 21
- Pages
- 216802-216802
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2113467957
- Cited by
- 2,033
- References
- 14
- Citations by year
- 2026: 54 · 2025: 60 · 2024: 62 · 2023: 68 · 2022: 85 · 2021: 101 · 2020: 134 · 2019: 102 · 2018: 95 · 2017: 121 · 2016: 134 · 2015: 130 · 2014: 142 · 2013: 146 · 2012: 145
- FWCI
- 55.56
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- Research Explorer (The University of Manchester) (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- DIGITAL.CSIC (Spanish National Research Council (CSIC)) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Bulletin of the American Physical Society
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Graphene research and applications
- Physical Sciences › Materials Science › Materials Chemistry › 2D Materials and Applications
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Quantum and electron transport phenomena
- Keywords
- bilayer graphene, electric field effects, band gap tuning, gate bias, Shubnikov-de Haas effect, cyclotron mass, tight-binding model, quantum Hall effect, electron density
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